e AM and FM radio waves are transverse waves consisting of
electric and magnetic disturbances traveling at a speed of 3.00 x 10
8
m/s. A
station broadcasts an AM radio wave whose frequency is 1230 x 10
3
Hz.
(1230 kHz on the dial) and an FM radio wave whose frequency is 99.1 x 10
6
Hz (99.1 MHz on the dial). Find the distance between adjacent crests in
each wave.
the distance between adjacent crests is the wavelangth λ.
λ1 =ñ/f1= 3•10^8/1230•10^3 = 243.9 m
λ2 =ñ/f2= 3•10^8/99.1•10^6 = 3.027 m
Waves moving on a lake have a speed of 2.0 m/s and a distance of 1.5 m between adjacent crests. (a) What is the frequency of the waves? (b) Find the period of the wave motion.
To find the distance between adjacent crests in each wave, we can use the formula:
wavelength = speed / frequency
For the AM radio wave:
Frequency = 1230 x 10^3 Hz
Using the formula, we can calculate the wavelength:
wavelength (AM wave) = (3.00 x 10^8 m/s) / (1230 x 10^3 Hz)
wavelength (AM wave) = 2.44 x 10^2 meters
Therefore, the distance between adjacent crests in the AM radio wave is approximately 244 meters.
For the FM radio wave:
Frequency = 99.1 x 10^6 Hz
Using the formula, we can calculate the wavelength:
wavelength (FM wave) = (3.00 x 10^8 m/s) / (99.1 x 10^6 Hz)
wavelength (FM wave) = 3.03 meters
Therefore, the distance between adjacent crests in the FM radio wave is approximately 3.03 meters.
To find the distance between adjacent crests in each wave, we need to use the formula:
wavelength = speed of light / frequency
Where:
- wavelength is the distance between adjacent crests
- speed of light is 3.00 x 10^8 m/s (given)
- frequency is the number of crests passing a point per second (given)
Let's calculate the wavelength for the AM radio wave:
Frequency of AM radio wave = 1230 x 10^3 Hz
wavelength_AM = (3.00 x 10^8 m/s) / (1230 x 10^3 Hz)
wavelength_AM = 2.44 x 10^2 m
Therefore, the distance between adjacent crests in the AM radio wave is 2.44 x 10^2 meters.
Now let's calculate the wavelength for the FM radio wave:
Frequency of FM radio wave = 99.1 x 10^6 Hz
wavelength_FM = (3.00 x 10^8 m/s) / (99.1 x 10^6 Hz)
wavelength_FM = 3.03 m
Therefore, the distance between adjacent crests in the FM radio wave is 3.03 meters.